Also remember that avenging Cat won't be something that is difficult for LF, as the lord of Harrenhal the Freys are subject to him, they answer to him. LF does not care for avenging Cat though, he now has Sansa to fill the void that Cat left.

I feel pretty nervous about Sansa standing in for Cat. LF is still engaged in exacting vengeance for himself. He was always out to hurt Cat ( through AGOT and beyond ) , and I don't think it would take much for Sansa to become a stand -in in that respect as well.

My opinion on this is quite mixed.
Maybe Littlefinger has probably played Catelyn for a fool and only used the notion of her being the love of his life. This is the least probable.
Then, what i think is more likely, Littlefinger might have been still in love with Catelyn throughout the books, but his affection might not have been so strong, so still he would only use Sansa for gaining power over the north...
But the most likely scenario is that Littlefinger strives for real vengeance. He knows the Game Of thrones, he knows the people who play it and he knows a great deal about the weaknesses and strengths of those people. At the same time his OWN only weakness ("the more people you love, the weaker you are" - Cersei) was his love for Catelyn. This exceptional relationship shows the other face of Littlefinger whom we primarily know as this scheming, clever and even dangerous man.
But to him this one love of his life seems to be the only thing he couldn't win with schemes. He tells Catelyn in Season two, that it appeares to him as if destiny brought them together.
And i think that he wants to have his revenge, for Catelyn through Sansa, but also for himself.

I believe LF's main goal is not the throne, but Winterfell. If he can have Winterfell, that means he has won, to him. As people have said, he has a deep resentment of highborns, but particularly the Starks. He'll show them, he himself will be the lord of Winterfell; and, Sansa is a stepping stone on that path. He didn't kill Joffrey and rescue Sansa "for his health", that's for sure. And, he didn't do it over remorse for what he did to the Starks and what happened to them generally. He risked a lot to do that, and I don't think the main goal was ridding the throne of Joffrey. I still wonder what connection, if any, that Varys and LF have in their goals. That idea raises many questions. I generally don't think they have any connection, but it's possible. To me, LF is still one of the most mysterious characters at the end of ADwD. It didn't shed much light on him. Perhaps he does want the throne, I just doubt he's aiming that high as of now. He has a lot of work to do before that, although that may be his endgame. He's well-informed and bright though, he may see that as an impossibility. He probably knows about Dany, "Aegon", Rickon, etc. It still bothers me that I have no idea what he truly wants.

Well,After Reading a feast of crows,I thought it was odd that Petyr never mentions anything about avenging cat.He obviously was deeply in love with her and I really expected that Petyr would device a plan to utterly destroy all who were Involved in the Red Wedding.I know he is calm and composed and wouldn't rush into doing anything he might resent later,But its the love of her life,the woman he was so devoted to that he challenged Brandon Stark for her hand.

Although nothing has been mentioned yet,But I do expect Petyr have some plan for revenge,something he reveals in later books.

I think Littlefinger loved Cat once upon a time. She became a symbol of something he wanted and couldn't have. In later life, he didn't even know who she was -- she is a conceptual conquest, I way of saying he won and beat the Starks/higher society.

Hmm.. But when he fought Brandon, didn't Cat ask Brandon to spare him , since he was "only a boy (or child?) ". I'd bet money that every action LF took involving Starks or Tullys , following that, was pure payback.

Before he kills Lysa, he tells her that Cat was the only woman he ever loved. His love for her was undeniably true. Revenge against Houses Stark and Tully is not quite as clear. He did offer Ned a deal to take the throne after all(which he should have taken).

Assuming he doesn't rape Sansa at some point, I think he sees her as the daughter that he should have had with Cat (or even a replacement for Cat). The Freys (like the Lannisters) are in major trouble. Half of their strength is soon likely to be lost in the North with Roose Bolton. The River Lords hate them (along with the rest of the realm) and are ready for revolt. Should LF's plans come to fruition and the he rallies the Vale, he could very well get revenge for Cat.

I think his love for Cat died a long time ago. All he has left is the obsession that he had for her, which he creepily transfers over to her daughter, Cat 2.0. I don't believe Littlefinger will ever try to avenge Cat. He only cares about revenge for himself - i.e. getting back at the people who "stole" Cat away from him.